{
  "id": 1761,
  "curve_key": "-29819391:195256472319",
  "ainvs": [
    "1",
    "-1",
    "1",
    "621237",
    "-226146597"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    7
  ],
  "naive_height": 51.995159547995435,
  "faltings_height": 2.4413067507826978,
  "conductor": "68354",
  "bad_primes": [
    "2",
    "11",
    "13",
    "239"
  ],
  "discriminant": "-37407624743081250944",
  "regulator": "8.050019047661590334242050981917971778151",
  "points": [
    [
      "38889/25",
      "8290302/125"
    ]
  ],
  "submitter": "hdeping",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-09-25 11:36:16"
    }
  ],
  "commentary": "Specialization t=13/2 of the universal X_1(7) Tate normal form family y^2+(-t^2+t+1)xy+(-t^3+t^2)y=x^3+(-t^3+t^2)x^2 (K3 elliptic surface, rational 7-torsion point (0,0)).",
  "created_at": "2026-09-25 11:26:42",
  "updated_at": "2026-09-25 11:36:16"
}